An ansatz for the exclusion statistics parameters in macroscopic physical systems described by fractional exclusion statistics

I introduce an ansatz for the exclusion statistics parameters of fractional exclusion statistics (FES) systems and I apply it to calculate the statistical distribution of particles from both, bosonic and fermionic perspectives. Then, to check the applicability of the ansatz, I calculate the FES parameters in three well-known models: in a Fermi liquid type of system, a one-dimensional quantum systems described in the thermodynamic Bethe ansatz and quasiparticle excitations in the fractional quantum Hall (FQH) systems. The FES parameters of the first two models satisfy the ansatz, whereas those of the third model, although close to the form given by the ansatz, represent an exception. With this ocasion I also show that the general properties of the FES parameters, deduced elsewhere (EPL 87, 60009, 2009), are satisfied also by the parameters of the FQH liquid.Comment: 6 pages, EPL styl

Universal behaviour of ideal and interacting quantum gases in two dimensions

I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the microscopic exclusion statistics, nor on the interaction. Such systems are called {\em thermodynamically equivalent} and I show that the microscopic reason for this equivalence is a one-to-one correspondence between the excited states of these systems. This provides a method, different from the bosonisation technique, to transform between systems of different exclusion statistics. In the last section the macroscopic aspects of this method are discussed. In Appendix A I calculate the fluctuation of the ground state population of a condensed Bose gas in grandcanonical ensemble and mean field approximation, while in Appendix B I show a situation where although the system exhibits fractional exclusion properties on microscopic energy intervals, a rigorous calculation of the population of single particle states reveals a condensation phenomenon. This also implies a malfunction of the usual and simplified calculation technique of the most probable statistical distributions.Comment: About 14 journal pages, with 1 figure. Changes: Body of paper: same content, with slight rephrasing. Apendices are new. In the original submission I just mentioned the condensation, which is now detailed in Appendix B. They were intended for a separate paper. Reason for changes: rejection from Phys. Rev. Lett., resubmission to J. Phys. A: Math. Ge

Power grids vulnerability: a complex network approach

Power grids exhibit patterns of reaction to outages similar to complex networks. Blackout sequences follow power laws, as complex systems operating near a critical point. Here, the tolerance of electric power grids to both accidental and malicious outages is analyzed in the framework of complex network theory. In particular, the quantity known as efficiency is modified by introducing a new concept of distance between nodes. As a result, a new parameter called net-ability is proposed to evaluate the performance of power grids. A comparison between efficiency and net-ability is provided by estimating the vulnerability of sample networks, in terms of both the metrics.Comment: 16 pages, 3 figures. Figure 2 and table II modified. Typos corrected. Version accepted for publication in Chao

Second order resonant Raman scattering in single layer tungsten disulfide (WS2_{2})

Resonant Raman spectra of single layer WS$_{2}$ flakes are presented. A second order Raman peak (2LA) appears under resonant excitation with a separation from the E$^{1}_{2g}$ mode of only $4$cm$^{-1}$. Depending on the intensity ratio and the respective line widths of these two peaks, any analysis which neglects the presence of the 2LA mode can lead to an inaccurate estimation of the position of the E$^{1}_{2g}$ mode, leading to a potentially incorrect assignment for the number of layers. Our results show that the intensity of the 2LA mode strongly depends on the angle between the linear polarization of the excitation and detection, a parameter which is neglected in many Raman studies.Comment: 6 pages, 4 figure

Condensation in ideal Fermi gases

I investigate the possibility of condensation in ideal Fermi systems of general single particle density of states. For this I calculate the probability $w_{N_0}$ of having exactly $N_0$ particles in the condensate and analyze its maxima. The existence of such maxima at macroscopic values of $N_0$ indicates a condensate. An interesting situation occurs for example in 1D systems, where $w_{N_0}$ may have two maxima. One is at $N_0=0$ and another one may exist at finite $N_0$ (for temperatures bellow a certain condensation temperature). This suggests the existence of a first order phase transition. % The calculation of $w_{N_0}$ allows for the exploration of ensemble equivalence of Fermi systems from a new perspective.Comment: 8 pages with 1 figure. Will appear in J. Phys. A: Math. Gen. Changes (minor): I updated Ref. [9] and its citation in the text. I introduced citation for figure 1 in the tex